Fast frequency sweeps with many forcing vectors through adaptive interpolatory model order reduction

Abstract

SUMMARYThe goal of this work is to examine the efficacy of interpolatory model order reduction on frequency sweep problems with many forcing vectors. The adaptive method proposed relies on the implicit interpolatory properties of subspace projection with basis vectors spanning the forced response of the system and its derivatives. The algorithm is similar to a recently proposed adaptive scheme in that it determines both interpolation location and order within the frequency domain of interest. The bounds of efficiency of the approach as the number of forcing vectors grows are explored through the use of rough floating operation counts. This, in turn, guides choices made in the adaptive algorithm, including a new technique that prevents excessive subspace growth by capitalizing on subspace direction coupling. In order to demonstrate the algorithm's utility, a series of frequency sweep problems drawn from the field of structural acoustics is analyzed. It is demonstrated that increased order of interpolation can actually degrade the efficiency of the algorithm as the number of forcing vectors grows but that this can be limited by the subspace size throttling procedure developed here. Copyright © 2014 John Wiley & Sons, Ltd.

A greedy reduced basis scheme for multifrequency solution of structural acoustic systems

“…Detailed studies on the use of MOR in the context of fast frequency sweeps with FEM and many forcing vectors are available in the literature. 52,53 Similar studies are also planned for the herein presented greedy reduced basis scheme.…”

“…As a remedy, a truncated singular value decomposition could be applied in order to reduce the number of algebraically independent right‐hand sides. Detailed studies on the use of MOR in the context of fast frequency sweeps with FEM and many forcing vectors are available in the literature . Similar studies are also planned for the herein presented greedy reduced basis scheme.…”

An assessment of two popular Padé-based approaches for fast frequency sweeps of time-harmonic finite element problems

“…[1][2][3][4] The second approach focuses instead on the construction of a reduced sequence of vectors spanning a subspace on which the FE system can be projected, thus leading to a parametric sweep involving a reduced-size system. [5][6][7][8] While the former approach provides piecewise analytical expressions of the solution components, has been extended to multivariate problems, 9 and is very well suited for partial-field solutions, the latter method is potentially much more efficient, as also shown in the present contribution.…”